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Narrowing the complexity gap for colouring (C_s,P_t)-free graphs.

Huang, S. and Johnson, M. and Paulusma, D. (2014) 'Narrowing the complexity gap for colouring (C_s,P_t)-free graphs.', in 10th International Conference, AAIM 2014, Vancouver, BC, Canada, 8-11 July 2014 ; proceedings. Berlin, Heidelberg: Springer, pp. 162-173. Lecture notes in computer science. (8546).


Let k be a positive integer. The k-Colouring problem is to decide whether a graph has a k-colouring. The k-Precolouring Extension problem is to decide whether a colouring of a subset of a graph’s vertex set can be extended to a k-colouring of the whole graph. A k-list assignment of a graph is an allocation of a list — a subset of {1,…,k} — to each vertex, and the List k -Colouring problem asks whether the graph has a k-colouring in which each vertex is coloured with a colour from its list. We prove a number of new complexity results for these three decision problems when restricted to graphs that do not contain a cycle on s vertices or a path on t vertices as induced subgraphs (for fixed positive integers s and t).

Item Type:Book chapter
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Date accepted:No date available
Date deposited:15 January 2015
Date of first online publication:2014
Date first made open access:No date available

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